Question: Solve for $n$, $ -\dfrac{3}{n} = -\dfrac{n - 3}{5n} - \dfrac{4}{n} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $n$ $5n$ and $n$ The common denominator is $5n$ To get $5n$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ -\dfrac{3}{n} \times \dfrac{5}{5} = -\dfrac{15}{5n} $ The denominator of the second term is already $5n$ , so we don't need to change it. To get $5n$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{4}{n} \times \dfrac{5}{5} = -\dfrac{20}{5n} $ This give us: $ -\dfrac{15}{5n} = -\dfrac{n - 3}{5n} - \dfrac{20}{5n} $ If we multiply both sides of the equation by $5n$ , we get: $ -15 = -n + 3 - 20$ $ -15 = -n - 17$ $ 2 = -n $ $ n = -2$